Dielectric Filled Parallel Plate Capacitor Question

Feb 2011
I recently had a test in my Physics class and I answered this question wrong. I'm trying to figure out the correct solution so I can keep it in my records for future reference. I'm unsure how to set this up, I can't seem to find a way to solve it without a given value of Q.

"A parallel plate capacitor has rectangular plates measuring 44.0 cm by 30.0 cm, and can be charged to 1600 V maximum ΔV without electrical breakdown. The gap between the plates is fulled with mylar dielectric (κ=3.2). Find the thickness of the dielectric."

Any helps is appreciated.